Question

Two masses 90 kg and 160 kg are at a distance 5 m apart. Compute the magnitude of intensity of the gravitational field at a point distance 3m from the 90 kg and 4m from the 160 kg mass. G=6.67 $\times$ ${10}^{-11}$SI units..

• A. 9.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$
• B. 4.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$
• C. 6.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$
• D. 0.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

Answer 1

The correct option is A

9.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

Let A and B be the positions of the masses and P be the point at which the gravitational intensity is to be computed.

Gravitational intensity at P due to mass at A will be

$E_A$ =G$\frac{90}{3^2}$ = 10G,along PA.

Gravitational intensity at P due to mass at B will be

$E_n$ =G$\frac{160}{4^2}$ = 10G,alongPB.

In $\Delta 1APB,A{B}^2$ = $A{P}^2+P{B}^2$ ($\therefore$<$APB={90}^0)$

Therefore the magnitude of resultant gravitational intensity at P will be E = $\sqrt{{E_A}^2+{E_B}^2}$ = $\sqrt{(10G{)}^2+(10G{)}^2}$ = 10$\sqrt{2}$G

= 10$\sqrt{2}$ $\times$ 6.67 $\times$ ${10}^{-11}$ N/kg = 9.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$